Intersection Dimensions of Graph Classes

The intersection dimension of a graphG with respect to a classA of graphs is the minimumk such thatG is the intersection of at mostk graphs on vertex setV(G) each of which belongs toA. We consider the question when the intersection dimension of a certain family of graphs is bounded or unbounded. Our main results are (1) ifA is hereditary, i.e., closed on induced subgraphs, then the intersection dimension of all graphs with respect toA is unbounded, and (2) the intersection dimension of planar graphs with respect to the class of permutation graphs is bounded. We also give a simple argument based on [Ben-Arroyo Hartman, I., Newman, I., Ziv, R.:On grid intersection graphs, Discrete Math.87 (1991) 41-52] why the boxicity (i.e., the intersection dimension with respect to the class of interval graphs) of planar graphs is bounded. Further we study the relationships between intersection dimensions with respect to different classes of graphs.     

The Marica-Schonheim Inequality in Lattices

The Marica-Schönheim Inequality says that if A is a finitefamily of sets, then |A–||A| where A–A=[A₁\A₂:A₁,A₂A]. For a finite lattice L and AL, we define a–b=(J_a\J_b)where J_a=[jL:ja and j is join-irreducible], and if AL then welet A–A=[a₁–a₂: a₁, a₂A]. Then the analogue of theMarica-Schöonheim Inequality is |A–A|A| for all AL.We prove that this is true if L is distributive or complementedand modular or L is a partition lattice.     

Systematic analysis of the PSI experiment to directly measure the sticking probabilityω s in dt fusion

Starting in 1989 an experiment was run at PSI to directly measure the final sticking probability in muon catalyzed dt fusion. This experiment was based on an active-target ionization chamber (IC) built at Gatchina, Russia, and an array of plastic neutron counters. In three runs approximately 5×10⁶ isolated alpha signals were recorded with around one half of these occurring in the inner chamber region where we have more complete understanding of the systematic errors. Particularly from a long run in 1992 we were able to obtain a very clean sticking peak of some 5000 events. However, to reach an accurate value of sticking, all systematic effects and several major backgrounds had to be understood in detail. To this end a Monte Carlo code was written to simulate the full electrostatic environment of the IC and to recreate completely each signal type including the actual tritium decay noise from the live experiment. A slightly model dependent value of approx. 0.56±0.04% is obtained for final sticking.     

Feasibility of an experiment to determine the branching ratio for the emission of a heavy neutrino after muon capture in3He

The triton energy of the muon capture reaction ³He t+v, where ³ He is the ground state of muonic³He, has been measured in order to investigate a possible heavy v admixture into the flavour with high sensitivity. ³ He has been formed via the pd fusion reaction by stopping ^– in an ionization chamber (IC) filled with an H/D gas mixture of 3% D concentration at a pressure of 161 bar. In a first short experiment 650 triton events were observed yielding an upper limit for the -heavy v mixing strength of 2.3×10^–3 atE _0v=60 MeV.     

Survey of experimental results on μCF including hyperfine effects

Complementary to the investigations of the most efficient dt cycle, also the other muon-induced fusion cycles in mixtures of hydrogen isotopes have been studied. The results of these dedicated experiments provide rich information about muon-induced few-body reactions and contribute significantly to a better overall understanding of CF. A summary of the recent progress will be presented. Special emphasis will be put on two characteristic examples, namely a new experimental approach to study the muonic cascade in H-D mixtures and the systematic study of hyperfine effects in muon-induced reactions.     

The kinetics of muon-catalyzed dt fusion

A main source of information about the muon-catalyzed fusion cycle in D-T mixtures are the cycling rates _c, which are characteristic for the kinetic equilibrium of states attained rapidly in dense targets. The measurement, analysis and interpretation of these rates will be discussed, concentrating on the extensive set of rates observed at PSI over the last decade in gaseous, liquid and solid targets.Invited talk presented by Peter Kammel.     

Herstellung von 6,14-Ethenomorphinan-Derivaten

Zusammenfassung Dihydronorthevinon (2b) wurde aus Dihydrothevinon (2a) mit Azodicarbonsäurediethylester (DEAD) hergestellt und zu einigen neuen N-substituierten Dihydronorthevinon-Derivaten (2c–2g) umgesetzt. Es wurdenGrignard-Reaktionen dieser Verbindungen mit Methylmagnesiumiodid bzw.tert-Butylmagnesiumchlorid durchgeführt. O-Demethylierungen von3a–3j ergaben die entsprechenden N-substituierten Buprenorphin- bzw. Diprenorphin-Analoga4a–4j.

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Preparation of 6,14-ethenomorphinan derivatives

Summary Dihydronorthevinone (2b) was prepared from dihydrothevinone (2a) with diethyl azodicarboxylate (DEAD) and transformed into a number of new N-substituted dihydronorthevinone derivatives (2c–2g).Grignard reactions of the new compounds with methylmagnesium iodide andtert-butyl-magnesium chloride were studied. O-Demethylation of3a–3j resulted in the corresponding N-substituted buprenorphine and diprenorphine analogs4a–4j.